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vovangra [49]
2 years ago
10

Rachael’s employer matches 16% of Rachel’s contribution to her 401k plan. If racheals employer contributed $400 to the plan a ye

ar , how much did racheal contribute to the plan last year
Mathematics
2 answers:
Butoxors [25]2 years ago
4 0
If x is Rachael's contributions
400=16%x
2,500=x

Rachael contributed $2,500 to her 401k last year
olga2289 [7]2 years ago
3 0

Answer:

$2500.

Step-by-step explanation:

Let x be represent the amount contributed by Rachael's to her 401(k) plan.

We have been given that Rachael’s employer matches 16% of Rachel’s contribution to her 401(k) plan. Rachael's employer contributed $400 to the plan a year.

We need to find x such that 16% of x is $400.

\frac{16}{100}*x=\$400

0.16*x=\$400

\frac{0.16*x}{0.16}=\frac{\$400}{0.16}

x=\$2500

Therefore, Rachael contributed $2500 to the plan last year.

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The expected value of the amount of average snowfall for over 30 years is 86.7 inches with a standard deviation of 40.4 inches. To verify if this particular trend continues, we must check the significance value of the amount snowfall for the past four years. Given that the snowfall for past years are as follows: 115.7 inches, 62.9 inches, 168.5 inches, and 135.7 inches. Thus the mean of the sample would be: (115.7 + 62.9 + 168.5 + 135.7)/4 = 120.7 inches. To compute for the z-score, we have z-score = (x – μ) / (σ / √n) where x is the computed/measured value, μ is the expected mean, σ is the standard deviation, and n is the number of samples. Using the information we have, z-score (z) = (120.7 - 86.7) / (40.4/ √4) = 1.68 In order to reject the null hyptohesis our probability value must be less than the significance level of 5%. For our case, since z = 1.68, P-value = 0.093 > 0.05. Therefore, the answer is B.
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2 years ago
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What is the exact value of the cos F?
Galina-37 [17]

Answer:

cos(F) = 9/41

Step-by-step explanation:

The triangles are similar, so you know that ...

... cos(D) = cos(A) = 40/41.

From trig relations, you know ...

... cos(F) = sin(D)

and

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So ...

... cos(F) = sin(D) = √(1 -cos(D)²) = √(1 -(40/41)²) = √(81/1681)

... cos(F) = 9/41

_____

The ratio for cos(A) tells you that you can consider AB=40, AC=41. Then, using the Pythagorean theorem, you can find BC = √(41² -40²) = √81 = 9.

From the definition of the cosine, you know cos(C) = BC/AC = 9/41. Because the triangles are similar, you know

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2 years ago
A student estimates the weight of astronauts on the moon by multiplying their weight by the decimal 0.16666....what fraction can
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Let x = 1.66666... ....(1)

Multiply both sides of equation (1) by 10.

10x = 1.666666.... .... (2)

Multiply both sides of equation (1) by 100.

100x = 16.66666....... (3)

Subtract equation (2) from equation (3)

100x - 10x = 16.66666...- 1.66666...

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x= \frac{15}{90}  = \frac{1}{6}

Hence, the required fraction form is \frac{1}{6} .... Answer.


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Find the sum of 67.008 and 3.8
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2 years ago
Tickets to a musical cost $30 for adults and $12 for children. At one particular performance 960 people attended and $19 080 was
postnew [5]
In order to solve this, you have to set up a systems of linear equations.

Let's say that children = c and adults = a

30a + 12c = 19,080
a + c = 960

I'm going to show you how to solve this system of linear equations by substitution, the easiest way to solve in my opinion.

   a + c = 960 
       - c    -    c
 ---------------------- ⇒ Step 1: Solve for either a or c in either equation.
   a = 960 - c 



20(960 - c)+ 12c = 19,080
19,200 - 20c + 12c = 19,080
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 - 19,200         - 19,200
---------------------------------- ⇒ Step 2: Substitute in the value you got for a or c
         8c = -120                    into the opposite equation.                                                
       ------  ---------
          8         8
 
         c = -15



30a + 12(-15) = 19,080
   30a - 180 = 19,080
          + 180  +     180
 -------------------------------
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  -------   -----------
    30          30
     
       a = 642
__________________________________________________________

I just realized that there can't be a negative amount of children, so I'm sorry if these results are all wrong. 


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1 year ago
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